√(7^2 . (2 - √5)^2)

First, let's simplify the expression inside the square root:

(7^2 . (2 - √5)^2) = (49 . (2 - √5)^2)

Next, let's expand the square:

(49 . (2 - √5)^2) = 49 . (2 - √5)(2 - √5)

Using the FOIL method to multiply the binomials:

49 . (2 - √5)(2 - √5) = 49 . (4 - 2√5 - 2√5 + 5)

Simplifying further:

49 . (4 - 2√5 - 2√5 + 5) = 49 . (9 - 4√5)

Now, let's simplify the expression inside the square root:

√(49 . (9 - 4√5)) = √(49) . √(9 - 4√5)

Taking the square root of 49:

√(49) = 7

Now, let's simplify the expression inside the square root:

√(9 - 4√5) = √(9) . √(1 - 4√5/9)

Taking the square root of 9:

√(9) = 3

Now, let's simplify the expression inside the square root:

√(1 - 4√5/9) = √(1 - (4√5/9))

Since we cannot simplify this expression any further, the final simplified form is:

7 * 3 * √(1 - (4√5/9))